UNIT OVERVIEW

In this unit, students build on their knowledge from Unit 2, where they extend the laws of exponents to rational exponents. Students strengthen their ability to see structure in and create quadratic and exponential expressions. They create and solve equations and inequalities involving quadratic expressions. Standard N.RN.2 was added to this unit by Maryland educators. This standard deals with simplifying and performing operation on radicals which is a skill that is useful when working with the quadratic formula and later in Geometry. Students learn that some quadratic equations have no real solutions. In Algebra II students will revisit quadratic equations. At that time they will learn to extend the number system to include complex numbers allowing them to determine two solutions for equations such as +1=0 .

Essential Questions:

When and how is mathematics used in solving real world problems?

How are linear, exponential and quadratic equations and inequalities used to solve real world problems?

What characteristics of problems would determine how to model the situation and develop a problem solving strategy?

What characteristics of problems would help to distinguish whether the situation could be modeled by a linear, exponential or a quadratic model?

When is it advantageous to represent relationships between quantities symbolically? Numerically? Graphically?

Why is it necessary to follow set rules/procedures/properties when manipulating numeric or algebraic expressions?

How can the representation of rational and irrational numbers help explain an appropriate strategy for simplification?

How can the structure of expressions, equations, or inequalities be used to determine a solution strategy?

How can quadratic and exponential expressions be rearranged to make it easier to indentify attributes of the expression?

A question is essential when it stimulates multi-layered inquiry, provokes deep thought and lively discussion, requires students to consider alternatives and justify their reasoning, encourges re-thinking of big ideas, makes meaningful connections with prior learning, and provides students with opportunities to apply problem-solving skills to authentic situations.

Additional information such as Teachers Notes, Enduring Understandings,Content Emphasis by Cluster, Focus Standards, Possible Student Outcomes, Essential Skills and Knowledge Statements and Clarifications, and Interdisciplinary Connections can be found in this Lesson Unit.